Neural Networksbased Random Vortex Methods for Modelling Incompressible Flows
Abstract
In this paper we introduce a novel Neural Networksbased approach for approximating solutions to the (2D) incompressible NavierStokes equations. Our algorithm uses a Physicsinformed Neural Network, that approximates the vorticity based on a loss function that uses a computationally efficient formulation of the Random Vortex dynamics. The neural vorticity estimator is then combined with traditional numerical PDEsolvers for the Poisson equation to compute the velocity field. The main advantage of our method compared to standard Physicsinformed Neural Networks is that it strictly enforces physical properties, such as incompressibility or boundary conditions, which might otherwise be hard to guarantee with purely Neural Networksbased approaches.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.13691
 arXiv:
 arXiv:2405.13691
 Bibcode:
 2024arXiv240513691C
 Keywords:

 Physics  Fluid Dynamics;
 Mathematics  Numerical Analysis;
 Mathematics  Probability;
 Statistics  Machine Learning;
 76M35;
 76M23;
 60H30;
 65C05;
 68Q10;
 68T07
 EPrint:
 16 pages, 5 figures